Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method

Maria Rosaria Formica; Eugeny Ostrovsky; Leonid Sirota

doi:10.1007/s10440-020-00339-5

Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method

Maria Rosaria Formica, Eugeny Ostrovsky, Leonid Sirota

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish also non-asymptotic, rapidly decreasing at infinity, upper and lower estimates for the fundamental solution. We extend the classical parametrix method of E.E. Levi.

Original language	English
Pages (from-to)	399-413
Number of pages	15
Journal	Acta Applicandae Mathematicae
Volume	170
Issue number	1
DOIs	https://doi.org/10.1007/s10440-020-00339-5
State	Published - 1 Dec 2020

Bibliographical note

Funding Information:
The first author has been partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Università degli Studi di Napoli Parthenope through the project “sostegno alla Ricerca individuale”.

Funding Information:
The first author has been partially supported by the Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Universit? degli Studi di Napoli Parthenope through the project ?sostegno alla Ricerca individuale?.

Publisher Copyright:
© 2020, Springer Nature B.V.

Keywords

Chapman-Kolmogorov equation
Fundamental solution
Generalized Mittag-Leffler function
Neumann series
Partial Differential Equation of parabolic type
Volterra’s integral equation

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10.1007/s10440-020-00339-5

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Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method. / Formica, Maria Rosaria; Ostrovsky, Eugeny; Sirota, Leonid.
In: Acta Applicandae Mathematicae, Vol. 170, No. 1, 01.12.2020, p. 399-413.

Research output: Contribution to journal › Article › peer-review

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Fundamental Solution for Cauchy Initial Value Problem for Parabolic PDEs with Discontinuous Unbounded First-Order Coefficient at the Origin. Extension of the Classical Parametrix Method

Abstract

Bibliographical note

Keywords

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